Golf has become an increasingly popular sport with both amateurs and professionals, which has spurred the development of a wide range of technologies related to the design and manufacture of golf balls to improve the flight performance of a golf ball. The flight performance of the golf ball is affected by a variety of factors including the weight, size, materials, dimple pattern, and external shape of the golf ball. The United States Golf Association (“USGA”) sets the limits for the maximum weight of a golf ball to 45.93 grams (1.62 oz) and the minimum diameter of a golf ball to 42.67 grams (1.680 oz). Golf ball manufacturers seek to improve the performance of golf balls by adjusting the materials and construction of the ball within USGA constraints, and adjusting the dimple pattern and dimple shape to enhance the aerodynamics.
There are two important dimensionless parameters related to golf ball aerodynamics: the Reynolds number (Re=UD/v) and the dimensionless spinning rate (α=ω*D/(2U)). In these equations, U is the speed of the golf ball, D is the diameter of the golf ball, v is the kinematic viscosity of the air, and ω is the angular velocity of the golf ball. The Reynolds number Re measures the effect of inertial to viscous forces and is generally in the range of Re=80,000 to Re=250,000 during the flight of a golf ball. The spinning rate a is the ratio of the tangential rotational velocity of the golf ball to its translation speed and measures how fast the golf ball is spinning compared to its translational speed, and is generally between α=0.1 to α=0.3.
During the flight of a golf ball the air exerts a force on the golf ball that affects its trajectory. The aerodynamic force has three components as shown in FIG. 1. One component is the drag FD, which is parallel and opposite in direction to the motion of the golf ball GM. The other two components are the lift FL, which is perpendicular to the drag and is almost aligned with the vertical direction, and the lateral force FS, which is perpendicular to both the drag and lift forces (i.e., normal to the drawing page). The drag and lift coefficients CD and CL, respectively, are defined as CD=FD/(½ρU2), and CL=FL/(½ρU2), where ρ is the density of the air AM in which the golf ball GM is traveling.